{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Custom Widget\n",
    "## Exploring the Lorenz System of Differential Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this Notebook we explore the Lorenz system of differential equations:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} & = \\sigma(y-x) \\\\\n",
    "\\dot{y} & = \\rho x - y - xz \\\\\n",
    "\\dot{z} & = -\\beta z + xy\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the parameters ($\\sigma$, $\\beta$, $\\rho$) are varied."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we import the needed things from IPython, [NumPy](http://www.numpy.org/), [Matplotlib](http://matplotlib.org/index.html) and [SciPy](http://www.scipy.org/). Check out the class [Python for Data Science and Machine Learning Bootcamp](https://www.udemy.com/python-for-data-science-and-machine-learning-bootcamp/) if you're interested in learning more about this part of Python!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact, interactive\n",
    "from IPython.display import clear_output, display, HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib.colors import cnames\n",
    "from matplotlib import animation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the trajectories and plotting the result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a function that can integrate the differential equations numerically and then plot the solutions. This function has arguments that control the parameters of the differential equation ($\\sigma$, $\\beta$, $\\rho$), the numerical integration (`N`, `max_time`) and the visualization (`angle`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):\n",
    "\n",
    "    fig = plt.figure();\n",
    "    ax = fig.add_axes([0, 0, 1, 1], projection='3d');\n",
    "    ax.axis('off')\n",
    "\n",
    "    # prepare the axes limits\n",
    "    ax.set_xlim((-25, 25))\n",
    "    ax.set_ylim((-35, 35))\n",
    "    ax.set_zlim((5, 55))\n",
    "    \n",
    "    def lorenz_deriv(x_y_z, t0, sigma=sigma, beta=beta, rho=rho):\n",
    "        \"\"\"Compute the time-derivative of a Lorenz system.\"\"\"\n",
    "        x, y, z = x_y_z\n",
    "        return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n",
    "\n",
    "    # Choose random starting points, uniformly distributed from -15 to 15\n",
    "    np.random.seed(1)\n",
    "    x0 = -15 + 30 * np.random.random((N, 3))\n",
    "\n",
    "    # Solve for the trajectories\n",
    "    t = np.linspace(0, max_time, int(250*max_time))\n",
    "    x_t = np.asarray([integrate.odeint(lorenz_deriv, x0i, t)\n",
    "                      for x0i in x0])\n",
    "    \n",
    "    # choose a different color for each trajectory\n",
    "    colors = plt.cm.jet(np.linspace(0, 1, N));\n",
    "\n",
    "    for i in range(N):\n",
    "        x, y, z = x_t[i,:,:].T\n",
    "        lines = ax.plot(x, y, z, '-', c=colors[i])\n",
    "        _ = plt.setp(lines, linewidth=2);\n",
    "\n",
    "    ax.view_init(30, angle)\n",
    "    _ = plt.show();\n",
    "\n",
    "    return t, x_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's call the function once to view the solutions. For this set of parameters, we see the trajectories swirling around two points, called attractors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ac822183c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, x_t = solve_lorenz(angle=0, N=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using IPython's `interactive` function, we can explore how the trajectories behave as we change the various parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8c6fcac683e54aebb53559937774065e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=10, description='N', max=50), FloatSlider(value=0.0, description='angle', max=360.0), FloatSlider(value=4.0, description='max_time', max=12.0, min=-4.0), FloatSlider(value=10.0, description='sigma', max=50.0), FloatSlider(value=2.6666666666666665, description='beta', max=8.0, min=-2.6666666666666665), FloatSlider(value=28.0, description='rho', max=50.0), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))\n",
    "display(w);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object returned by `interactive` is a `Widget` object and it has attributes that contain the current result and arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, x_t = w.result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'N': 10,\n",
       " 'angle': 0.0,\n",
       " 'beta': 2.6666666666666665,\n",
       " 'max_time': 4.0,\n",
       " 'rho': 28.0,\n",
       " 'sigma': 10.0}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.kwargs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in $x$, $y$ and $z$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "xyz_avg = x_t.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xyz_avg.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating histograms of the average positions (across different trajectories) show that on average the trajectories swirl about the attractors.\n",
    "\n",
    "*NOTE: These will look different from the lecture version if you adjusted any of the sliders in the* `interactive` *widget and changed the parameters.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEKCAYAAAAVaT4rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAFsNJREFUeJzt3X20XXV95/H3x/Cg4xNorlbzQHCKjiiC9hp10Y5YFIJaYjuumcQHotWVpSNWZ9qZgq6RGZwHldankRZTjeiooKK0aRvFtIp0qtEkiCggGqM11+hwJahUHGnwO3+cfZ3Dzb25+957knOT/X6tdVbO/v1+e+/vuVw+Z9/f2WfvVBWSpO64z7ALkCQdWga/JHWMwS9JHWPwS1LHGPyS1DEGvyR1jMEvSR1j8EtSxxj80gKT5H8kee0MY76U5HGHqiYdWQx+HRaSXJvkjiTHDruWgynJCHAe8O5J7d9Lclpf0x8BFx/K2nTkMPi14CVZAfwGUMC5B2H7Rw16m/PwEmBzVf1soiHJYuBhwC194zYBz0jyiENbno4EBr8OB+cBW4HLgXUTjUkuSHJV/8Ak70jyzub5I5N8PMl4km8n+b2+cd9J8odJbgR+muSoZnvfSnJnkpuT/Hbf+Ccl+XLT97EkH0nyX/v6p93XZEnekuTqvuVLkvxtkqOBc4DP9fX9KrCb3v+rtye5PclRVfV/gR3AWbP9YUoGvw4H5wEfah5nJ3l4034F8OwkDwJIsgj418CHk9wH+EvgK8AS4EzgtUnO7tvuWuA5wHFVtQ/4Fr2/LB4M/Bfgg0kekeQY4Gp6bzwPafbb/6bQZl/93kzvaP20JK8AVgG/U1X/BJwC3DoxsKp2An8AXFVVD6iqhza1Qu8vgFNb/gylXzL4taAl+XXgBOCjVbWDXji/AKCq/gG4HnheM/w3gbuqaivwZGCkqi6uqrurahfwZ8Cavs2/s6p2T0yrVNXHqmpPVf2iqj4CfBNYCTwVOKoZ/09V9QngS33babOvX6qq24G3Ax8ALgSeXVU/brqPA+6ctMqpwA1TbOrOZrw0Kwa/Frp1wKer6ofN8ofpm+5pltc2z1/QLEPvzeKRSX408QBeBzy8b93d/TtKcl6SG/rGPx5YDDwS+F7d+xrm/eu22ddkX6Z3dH9hVfVv6w7ggZPGnkbvr4nJHgj86AD7kKa0kD7Uku4lyf3oTd0sSvKDpvlY4Lgkp1bVV4CPAX+cZCm96ZenNeN2A9+uqpMOsItfBnmSE+gdpZ8JfKGq7klyAxDg+8CSJOkL/2X0/vpou6/+13UK8KfA+4Hf5f+/WQHcCDwa2NaMvQ+9N6CpjvgfC3ywzT6lfh7xayF7HnAPcDK9o97T6IXd39Gb96eqxoFrgffRC9+JM1++BPyk+QD3fkkWJXl8kidPs6/703sjGAdI8lJ6gQvwhaaO85sPgVfTmwKa0HpfSZbQ+zzgFcC/BU5JckbfkM3A0/uW79c87vX/anNa668BW6Z5PdK0DH4tZOuA91XVd6vqBxMP4F3AC/tOw/ww8Ez6jpyr6h7gt+i9WXwb+CHwHnof3O6nqm4G/pheyP8fetMwf9/03Q38DvAyelMrLwL+Cvj5bPbVfAi9GXhrVW2qqruAS4D/1jfsA/Q+sL5fs+2fApcBNycZ6xt3LnBtVe2Z4Wco7SfeelGavSRfBC6rqvcdhG3/d+C2qnr7DPt/WVV9bdD715HP4JdaSPJ0eqdZ/hB4Ib2j8EdV1feHWpg0B364K7XzGOCjwAPofaj7fENfhyuP+CWpY/xwV5I6ZkFO9SxevLhWrFgx7DIk6bCxY8eOH1bVSJuxCzL4V6xYwfbt24ddhiQdNpL8Q9uxTvVIUscY/JLUMQa/JHWMwS9JHWPwS1LHGPyS1DEzBn+SZUk+m+SWJDclec0UY5LknUl2JrkxyZP6+tYl+WbzWDd5XUnSodXmPP59wO9X1fVJHgjsSLKluYzthHOAk5rHU+jdZOIpSR4CXASM0rvW+Y4km6rqjoG+CklSazMe8VfV96vq+ub5nfRu8Lxk0rDVwAeqZyu9OyQ9Ajgb2FJVe5uw30LvxtKSpCGZ1Td3k6wAngh8cVLXEu59D9Kxpm269qm2vR5YD7B8+fLZlHUvKy746zmvOx/fedNzhrJfdcOwfq+hm7/bR3qOtP5wN8kDgI8Dr62qn0zunmKVOkD7/o1VG6pqtKpGR0ZaXW5CkjQHrYI/ydH0Qv9DVfWJKYaM0bv59ISlwJ4DtEuShqTNWT0B3gvcUlVvnWbYJuC85uyepwI/bm5ScQ1wVpLjkxwPnNW0SZKGpM0c/+nAi4GvJrmhaXsdsBygqi6jdwPpZwM7gbuAlzZ9e5O8EdjWrHdxVe0dXPmSpNmaMfir6n8z9Vx9/5gCXjVN30Zg45yqkyQNnN/claSOMfglqWMMfknqGINfkjrG4JekjjH4JaljDH5J6hiDX5I6xuCXpI4x+CWpYwx+SeoYg1+SOsbgl6SOMfglqWMMfknqGINfkjpmxhuxJNkIPBe4raoeP0X/fwBe2Le9xwIjzd23vgPcCdwD7Kuq0UEVLkmamzZH/JcDq6brrKpLquq0qjoNuBD43KTbKz6j6Tf0JWkBmDH4q+o6oO19ctcCV8yrIknSQTWwOf4k/4zeXwYf72su4NNJdiRZP6h9SZLmbsY5/ln4LeDvJ03znF5Ve5I8DNiS5OvNXxD7ad4Y1gMsX758gGVJkvoN8qyeNUya5qmqPc2/twFXAyunW7mqNlTVaFWNjoyMDLAsSVK/gQR/kgcDTwf+oq/t/kkeOPEcOAv42iD2J0mauzanc14BnAEsTjIGXAQcDVBVlzXDfhv4dFX9tG/VhwNXJ5nYz4er6lODK12SNBczBn9VrW0x5nJ6p332t+0CTp1rYZKkg8Nv7kpSxxj8ktQxBr8kdYzBL0kdY/BLUscY/JLUMQa/JHWMwS9JHWPwS1LHGPyS1DEGvyR1jMEvSR1j8EtSxxj8ktQxBr8kdYzBL0kdY/BLUsfMGPxJNia5LcmU98tNckaSHye5oXm8oa9vVZJbk+xMcsEgC5ckzU2bI/7LgVUzjPm7qjqteVwMkGQRcClwDnAysDbJyfMpVpI0fzMGf1VdB+ydw7ZXAjuraldV3Q1cCayew3YkSQM0qDn+pyX5SpJPJnlc07YE2N03Zqxpm1KS9Um2J9k+Pj4+oLIkSZMNIvivB06oqlOB/wn8edOeKcbWdBupqg1VNVpVoyMjIwMoS5I0lXkHf1X9pKr+sXm+GTg6yWJ6R/jL+oYuBfbMd3+SpPmZd/An+ZUkaZ6vbLZ5O7ANOCnJiUmOAdYAm+a7P0nS/Bw104AkVwBnAIuTjAEXAUcDVNVlwPOBVybZB/wMWFNVBexLcj5wDbAI2FhVNx2UVyFJam3G4K+qtTP0vwt41zR9m4HNcytNknQw+M1dSeoYg1+SOsbgl6SOMfglqWMMfknqGINfkjrG4JekjjH4JaljDH5J6hiDX5I6xuCXpI4x+CWpYwx+SeoYg1+SOsbgl6SOMfglqWMMfknqmBmDP8nGJLcl+do0/S9McmPz+HySU/v6vpPkq0luSLJ9kIVLkuamzRH/5cCqA/R/G3h6VT0BeCOwYVL/M6rqtKoanVuJkqRBanPP3euSrDhA/+f7FrcCS+dfliTpYBn0HP/LgE/2LRfw6SQ7kqw/0IpJ1ifZnmT7+Pj4gMuSJE2Y8Yi/rSTPoBf8v97XfHpV7UnyMGBLkq9X1XVTrV9VG2imiUZHR2tQdUmS7m0gR/xJngC8B1hdVbdPtFfVnubf24CrgZWD2J8kae7mHfxJlgOfAF5cVd/oa79/kgdOPAfOAqY8M0iSdOjMONWT5ArgDGBxkjHgIuBogKq6DHgD8FDgT5IA7GvO4Hk4cHXTdhTw4ar61EF4DZKkWWhzVs/aGfpfDrx8ivZdwKn7ryFJGia/uStJHWPwS1LHGPyS1DEGvyR1jMEvSR1j8EtSxxj8ktQxBr8kdYzBL0kdY/BLUscY/JLUMQa/JHWMwS9JHWPwS1LHGPyS1DEGvyR1jMEvSR3TKviTbExyW5Ip75mbnncm2ZnkxiRP6utbl+SbzWPdoAqXJM1N2yP+y4FVB+g/BzipeawH/hQgyUPo3aP3KcBK4KIkx8+1WEnS/LUK/qq6Dth7gCGrgQ9Uz1bguCSPAM4GtlTV3qq6A9jCgd9AJEkH2Yw3W29pCbC7b3msaZuufT9J1tP7a4Hly5cPqKxDZ8UFfz20fX/nTc8Zyn6H+Zolzd2gPtzNFG11gPb9G6s2VNVoVY2OjIwMqCxJ0mSDCv4xYFnf8lJgzwHaJUlDMqjg3wSc15zd81Tgx1X1feAa4Kwkxzcf6p7VtEmShqTVHH+SK4AzgMVJxuidqXM0QFVdBmwGng3sBO4CXtr07U3yRmBbs6mLq+pAHxJLkg6yVsFfVWtn6C/gVdP0bQQ2zr40SdLB4Dd3JaljDH5J6hiDX5I6xuCXpI4x+CWpYwx+SeoYg1+SOsbgl6SOMfglqWMMfknqGINfkjrG4JekjjH4JaljDH5J6hiDX5I6xuCXpI4x+CWpY1oFf5JVSW5NsjPJBVP0vy3JDc3jG0l+1Nd3T1/fpkEWL0mavRlvvZhkEXAp8CxgDNiWZFNV3Twxpqr+Xd/4VwNP7NvEz6rqtMGVLEmajzZH/CuBnVW1q6ruBq4EVh9g/FrgikEUJ0kavDbBvwTY3bc81rTtJ8kJwInAZ/qa75tke5KtSZ433U6SrG/GbR8fH29RliRpLtoEf6Zoq2nGrgGuqqp7+tqWV9Uo8ALg7Un++VQrVtWGqhqtqtGRkZEWZUmS5qJN8I8By/qWlwJ7phm7hknTPFW1p/l3F3At957/lyQdYm2CfxtwUpITkxxDL9z3OzsnyWOA44Ev9LUdn+TY5vli4HTg5snrSpIOnRnP6qmqfUnOB64BFgEbq+qmJBcD26tq4k1gLXBlVfVPAz0WeHeSX9B7k3lT/9lAkqRDb8bgB6iqzcDmSW1vmLT8n6dY7/PAKfOoT5I0YH5zV5I6xuCXpI4x+CWpYwx+SeoYg1+SOsbgl6SOMfglqWMMfknqGINfkjrG4JekjjH4JaljDH5J6hiDX5I6xuCXpI4x+CWpYwx+SeoYg1+SOqZV8CdZleTWJDuTXDBF/0uSjCe5oXm8vK9vXZJvNo91gyxekjR7M956Mcki4FLgWcAYsC3JpinunfuRqjp/0roPAS4CRoECdjTr3jGQ6iVJs9bmiH8lsLOqdlXV3cCVwOqW2z8b2FJVe5uw3wKsmlupkqRBaBP8S4DdfctjTdtk/yrJjUmuSrJsluuSZH2S7Um2j4+PtyhLkjQXbYI/U7TVpOW/BFZU1ROAvwHeP4t1e41VG6pqtKpGR0ZGWpQlSZqLNsE/BizrW14K7OkfUFW3V9XPm8U/A36t7bqSpEOrTfBvA05KcmKSY4A1wKb+AUke0bd4LnBL8/wa4Kwkxyc5HjiraZMkDcmMZ/VU1b4k59ML7EXAxqq6KcnFwPaq2gT8XpJzgX3AXuAlzbp7k7yR3psHwMVVtfcgvA5JUkszBj9AVW0GNk9qe0Pf8wuBC6dZdyOwcR41SpIGyG/uSlLHGPyS1DEGvyR1jMEvSR1j8EtSxxj8ktQxBr8kdYzBL0kdY/BLUscY/JLUMQa/JHWMwS9JHWPwS1LHGPyS1DEGvyR1jMEvSR1j8EtSx7QK/iSrktyaZGeSC6bo//dJbk5yY5K/TXJCX989SW5oHpsmrytJOrRmvPVikkXApcCzgDFgW5JNVXVz37AvA6NVdVeSVwJvAf5N0/ezqjptwHVLkuaozRH/SmBnVe2qqruBK4HV/QOq6rNVdVezuBVYOtgyJUmD0ib4lwC7+5bHmrbpvAz4ZN/yfZNsT7I1yfOmWynJ+mbc9vHx8RZlSZLmYsapHiBTtNWUA5MXAaPA0/ual1fVniSPAj6T5KtV9a39Nli1AdgAMDo6OuX2JUnz1+aIfwxY1re8FNgzeVCSZwKvB86tqp9PtFfVnubfXcC1wBPnUa8kaZ7aBP824KQkJyY5BlgD3OvsnCRPBN5NL/Rv62s/PsmxzfPFwOlA/4fCkqRDbMapnqral+R84BpgEbCxqm5KcjGwvao2AZcADwA+lgTgu1V1LvBY4N1JfkHvTeZNk84GkiQdYm3m+KmqzcDmSW1v6Hv+zGnW+zxwynwKlCQNlt/claSOMfglqWMMfknqGINfkjrG4JekjjH4JaljDH5J6hiDX5I6xuCXpI4x+CWpYwx+SeoYg1+SOsbgl6SOMfglqWMMfknqGINfkjrG4JekjmkV/ElWJbk1yc4kF0zRf2ySjzT9X0yyoq/vwqb91iRnD650SdJczBj8SRYBlwLnACcDa5OcPGnYy4A7qupXgbcBb27WPZnezdkfB6wC/qTZniRpSNoc8a8EdlbVrqq6G7gSWD1pzGrg/c3zq4Az07vr+mrgyqr6eVV9G9jZbE+SNCRtbra+BNjdtzwGPGW6MVW1L8mPgYc27Vsnrbtkqp0kWQ+sbxb/McmtLWo7kMXAD+e5jWFqXX/efJArmZvO/PwXqIHVP6Tfr07+/Of5sz6h7cA2wZ8p2qrlmDbr9hqrNgAbWtTTSpLtVTU6qO0datY/XNY/XNZ/cLWZ6hkDlvUtLwX2TDcmyVHAg4G9LdeVJB1CbYJ/G3BSkhOTHEPvw9pNk8ZsAtY1z58PfKaqqmlf05z1cyJwEvClwZQuSZqLGad6mjn784FrgEXAxqq6KcnFwPaq2gS8F/hfSXbSO9Jf06x7U5KPAjcD+4BXVdU9B+m1TDawaaMhsf7hsv7hsv6DKL0Dc0lSV/jNXUnqGINfkjrmiA7+JK9uLhVxU5K3DLueuUryB0kqyeJh1zIbSS5J8vUkNya5Oslxw66pjZkuUbKQJVmW5LNJbml+718z7JrmIsmiJF9O8lfDrmW2khyX5Krmd/+WJE8bdk2THbHBn+QZ9L45/ISqehzwR0MuaU6SLAOeBXx32LXMwRbg8VX1BOAbwIVDrmdGLS9RspDtA36/qh4LPBV41WFW/4TXALcMu4g5egfwqar6F8CpLMDXccQGP/BK4E1V9XOAqrptyPXM1duA/8g0X3xbyKrq01W1r1ncSu97HAtdm0uULFhV9f2qur55fie90Jny2/ILVZKlwHOA9wy7ltlK8iDgX9I705GquruqfjTcqvZ3JAf/o4HfaK4W+rkkTx52QbOV5Fzge1X1lWHXMgC/C3xy2EW0MNUlSg6r4JzQXCX3icAXh1vJrL2d3sHOL4ZdyBw8ChgH3tdMVb0nyf2HXdRkbS7ZsGAl+RvgV6boej2913Y8vT93nwx8NMmjaoGdvzrDa3gdcNahrWh2DlR/Vf1FM+b19KYgPnQoa5uj1pcZWciSPAD4OPDaqvrJsOtpK8lzgduqakeSM4ZdzxwcBTwJeHVVfTHJO4ALgP803LLu7bAO/qp65nR9SV4JfKIJ+i8l+QW9CyeNH6r62pjuNSQ5BTgR+ErvQqcsBa5PsrKqfnAISzygA/03AEiyDngucOZCe9OdxmF/mZEkR9ML/Q9V1SeGXc8snQ6cm+TZwH2BByX5YFW9aMh1tTUGjFXVxF9ZV9EL/gXlSJ7q+XPgNwGSPBo4hsPoan9V9dWqelhVraiqFfR+oZ60kEJ/JklWAX8InFtVdw27npbaXKJkwWouh/5e4Jaqeuuw65mtqrqwqpY2v/Nr6F3+5XAJfZr/P3cneUzTdCa9KxcsKIf1Ef8MNgIbk3wNuBtYd5gccR5J3gUcC2xp/mrZWlWvGG5JBzbdJUqGXNZsnA68GPhqkhuattdV1eYh1tQ1rwY+1Bw47AJeOuR69uMlGySpY47kqR5J0hQMfknqGINfkjrG4JekjjH4JaljDH5J6hiDX5I65v8BiUMB92RDABsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ac824c48d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(xyz_avg[:,0])\n",
    "plt.title('Average $x(t)$');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ac82e62e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(xyz_avg[:,1])\n",
    "plt.title('Average $y(t)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "Hopefully you've enjoyed using widgets in the Jupyter Notebook system and have begun to explore the other GUI possibilities for Python!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
